16.050 Thermal Energy
Recitation #2 – Fall 2002
Problem 1:
The core of a certain gas turbine system, as drawn on the board, has a compressor, a combustor, and a turbine. You are given the following system specifications: Tta= 300 K (compressor inlet total temperature) Ttc= 1800 K (high pressure turbine inlet total temperature) rc= 15 (compressor total pressure ratio) m = 75 kg/s Pta=Ptd=1 bar You may assume that air behaves as an ideal gas with cp=1000 J/kgK everywhere. You may assume that the compressor and turbine are reversible. a) What is the power output of the system?
b) What is the efficiency of the gas turbine system?
Suppose an ideal regenerator (100% regeneration) is added to the system as shown on
the board.
c) What is the efficiency of the cycle with the regenerator added?
d) Assuming the cycle produce the same power, what is the difference
between the heat input required, without and with the regenerator?
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Problem 2:
A certain fuel burns at a temperature of 2100 K producing 45 kJ/kg of heat. It is
proposed to operate a Carnot heat engine between the burning fuel and the atmosphere
at T=300 K (80 F). Determine the work output of this heat engine.
The work output from the heat engine is used to drive a Carnot refrigerator. The
refrigerator is used to cool a room at a constant temperature of 290 K (62 F), and rejects
heat to the same atmosphere. Find:
a) The coefficient of performance (COP).
b) The amount of heat removed from the room in kJ/kg.
Now, suppose that the atmosphere temperature has increased to 310 K (98 F) on a hot
summer day. Assuming that the refrigerator removes the same amount of heat from the
room, determine the work in kJ/kg required to drive the refrigerator.
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